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On the computation of eigen modes for lossy microwave transmission lines including perfectly matched layer boundary conditions

On the computation of eigen modes for lossy microwave transmission lines including perfectly... The design of microwave circuits requires detailed knowledge on the electromagnetic properties of the transmission lines used. This can be obtained by applying Maxwell’s equations to a longitudinally homogeneous waveguide structure, which results in an eigenvalue problem for the propagation constant. Special attention is paid to the so‐called perfectly matched layer boundary conditions (PML). Using the finite integration technique we get an algebraic formulation. The finite volume of the PML introduces additional modes that are not an intrinsic property of the waveguide. In the presence of losses or absorbing boundary conditions the matrix of the eigenvalue problem is complex. A method which avoids the computation of all eigenvalues is presented in an effort to find the few propagating modes one is interested in. This method is an extension of a solver presented by the authors in a previous paper which analyses the lossless case. Using mapping relations between the planes of eigenvalues and propagation constants a strip in the complex plane is determined containing the desired propagation constants and some that correspond to the PML modes. In an additional step the PML modes are eliminated.The numerical effort of the presented method is reduced considerably compared to a full calculation of all eigenvalues. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

On the computation of eigen modes for lossy microwave transmission lines including perfectly matched layer boundary conditions

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References (16)

Publisher
Emerald Publishing
Copyright
Copyright © 2001 MCB UP Ltd. All rights reserved.
ISSN
0332-1649
DOI
10.1108/EUM0000000005770
Publisher site
See Article on Publisher Site

Abstract

The design of microwave circuits requires detailed knowledge on the electromagnetic properties of the transmission lines used. This can be obtained by applying Maxwell’s equations to a longitudinally homogeneous waveguide structure, which results in an eigenvalue problem for the propagation constant. Special attention is paid to the so‐called perfectly matched layer boundary conditions (PML). Using the finite integration technique we get an algebraic formulation. The finite volume of the PML introduces additional modes that are not an intrinsic property of the waveguide. In the presence of losses or absorbing boundary conditions the matrix of the eigenvalue problem is complex. A method which avoids the computation of all eigenvalues is presented in an effort to find the few propagating modes one is interested in. This method is an extension of a solver presented by the authors in a previous paper which analyses the lossless case. Using mapping relations between the planes of eigenvalues and propagation constants a strip in the complex plane is determined containing the desired propagation constants and some that correspond to the PML modes. In an additional step the PML modes are eliminated.The numerical effort of the presented method is reduced considerably compared to a full calculation of all eigenvalues.

Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering – Emerald Publishing

Published: Dec 1, 2001

Keywords: Microwaves; Maxwell’s theory; Boundary conditions; Integration; Eigenvalues

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